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Derivative of Sine Using Limit Definition

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Using the graph of f(x)=sin⁡(x)f(x)=\sin(x), find the derivative f′(x)f'(x) using the limit definition of the derivative.

A

−cos⁡(x)-\cos(x)

B

A misapplication might yield cos⁡(x)−sin⁡(x)\cos(x)-\sin(x), which is incorrect.

C

sin⁡(x)\sin(x)

D

cos⁡(x)\cos(x)

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